320 ON THE CHANGE OF REFRANGIBTLITY OF LIGHT.
the refrangibility of light be measured as before, and suppose for simplicity's sake the intensity of the incident light to be independent of the refrangibility, so that dy may be taken to represent the quantity of incident light of which the refrangibility lies between y and y + dy. Considering the effect of this portion of the incident light by itself, let x be the refrangibility of any portion of the dispersed light, and zdxdy the quantity of dispersed light of which the refrangibility lies between x and x + dx. Then the curved surface, of which the coordinates are a?, y, z, will represent the nature of the internal dispersion of the medium. We must suppose the intensity of the incident light referred to some standard independent of the eye, since the illuminating power of the rays beyond the violet, and even of the extreme violet, is utterly disproportionate to the effect which in these phenomena they produce.
From the nature of the case, the ordinate z of the surface can never be negative. The law mentioned in Art. 80 may be expressed by saying, that if we draw through the axis of z a plane bisecting the angle between the axes of x and y, at all points on the side of this plane towards x positive, the curved surface confounds itself with the plane of xy.
85. Let us consider the form of this surface in two or three instances of internal dispersion. For facility of explanation, suppose the plane of x\j horizontal, let ,/• be measured to the right, ?/ forwards, and z upwards. Let a line drawn in the plane of xy through the origin, and bisecting the angle between the axes of x and ?/, be called for shortness the lino L. In all cases the surface rises above the plane of x\j only to the left of the line L.
In the case of a solution of loaf-green, the surface consists as it were of two mountain ranges running in a direction parallel to the axis of ;y, or nearly so. The first range, if prolonged, would meet the axis of x at a point corresponding to the place of the dark band No. 1 in the red, or nearly so. The second would meet it somewhere in the place corresponding to the green. The green range is much broader than the red, but very much lower, and is comparatively insignificant. The ridge of the red range is by no means uniform, but presents a, succession of maxima and minima. The range commences at the end nearest to the axis of x with a very high peak, by far the highest in the whole surface. In